### MAT 157

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Question 1

An economics professor randomly selected 100 millionaires in the U.S. The average age of these millionaires was 52.1 years with a standard deviation of 12.3 years. What is the 95% lower confidence limit for the mean age, , of all U.S. millionaires?

Question 2

The following list is a sampling of the costs of various statistics textbooks used at several colleges. Give the upper confidence limit for a 95% confidence interval estimate for the mean cost of all statistics textbooks.

109.95; 92.00; 96.70; 84.85; 92.60; 84.45; 90.95; 77.00; 75.50

Question 3

What is the value for right for a 95% confidence interval when n = 24?

Question 4

A manufacturer of light bulbs claims that their light bulbs have a mean life of 1150 hours with a population standard deviation of 80 hours. A random testing of 144 light bulbs had a mean life of 1125 hours. Give the test value that would be used for a hypothesis test.

Question 5

A doctor believes that the variance of systolic blood pressure is 470. A random sample of 20 patients found a variance of 525. What is the smaller critical value that would be used in a hypothesis test at a .05 significance level?

Question 6

A random sample of 500 shoppers at South Mall found that 145 favored longer shopping hours. It is claimed that fewer than 33% of the shoppers at South Mall favor longer hours. Give the test value that would be used for a hypothesis test.

Question 7

At a .05 level of significance, the Department of Transportation claims that there is no difference between the variation of federal highway money distributed to the northeastern states and the variation of federal money distributed to the central states. The standard deviation for 11 northeastern states is 0.81 and the standard deviation for 12 central states is 0.35. What is the test value?

Question 8

The Department of Transportation claims that there is no difference between the variation of federal highway money distributed to the northeastern states and the variation of federal money distributed to the central states. The standard deviation for 11 northeastern states is 0.81 and the standard deviation for 12 central states is 0.35. Using a 5% level, what is the critical value?

Question 9

The registrar at a commuter college wanted to determine if there was a difference in the average number of hours students were working in two different classes. See the data below. For a level of significance of 0.05, what is the t-test value?

Class A

Class B

x=26.56

x=22.80

s=10.70

s=5.40

n=16

n=10

Question 10

The data gathered below gives the textbook costs for two groups of randomly selected students, from 1998 and 1999. A claim that students paid the same average will be conducted. Give the test value.

1998:

234

201

158

127

97

1999:

270

200

295

294

Question 1

Which of the following could not be the value of a correlation coefficient?

Question 2

Ten pairs of points yielded a correlation coefficient, r, of 0.79. Using a .05 significance level, which of the following statements is correct?

Question 3

A correlation coefficient computed for n = 18 and a 10% significance level is 0.692. Using a t-test for significance of the correlation coefficient, what is the largest critical value?

Question 4

A psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded. Determine the slope of the regression line.

Hours Without Sleep

Number of Mistakes

32

6

38

8

48

13

24

5

46

7

Question 5

A sociologist wanted to determine whether there was a difference in the amount of time children aged 5-7 spent watching television each day. The following data was gathered(in minutes). What is the critical value if the sociologist wants to test the claim that children watch television pretty much the same amount each day of the week? Use a 5% level of significance.

Day

M

T

W

Th

F

Sat

Sun

No. of Min.

125

140

130

125

200

225

210

Question 6

A chewing gum manufacturer wishes to determine if her customers prefer one flavor gum to any other flavor. She selects a random sample of customers and records the flavor of gum that is purchased. Determine the test value for the data given. (Type and number of each sold: Spearmint 25; Wintergreen 32; Cherry 18; Cinnamon 43)

Question 7

An anatomy teacher hypothesizes that the final grades in her class are distributed as 10% A's, 23% B's, 45% C's, 14% D's, and 8% F's. What is the critical value if at the end of the semester she records the following grades? 6 A's, 14 B's, 22 C's, 8 D's, and 4 F's. Use a .05 significance level.

Question 8

A vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of beverage. The plan is to use a 5% significance level to test the belief that there is a difference in the mean amount of beverage for the three machines. The table below gives the data. What is the grand mean?

Machine A

Machine B

Machine C

11.8

11.7

12.2

12.1

11.9

12.1

12

11.7

12

11.9

11.8

11.9

12.1

12

12.2

Question 9

A store manager wants to see if there is a difference in the average time (in minutes) a customer has to wait in line for 4 of her checkers. At a 2.5% level of significance, what is the critical value?

Checker 1

Checker 2

Checker 3

Checker 4

3

3

2

2

5

5

3

3

4

2

5

4

6

3

6

4

7

4

3

5

Question 10

Three categories are to be tested, at a 5% level of significance, to see if they have the same averages. The data appears in the table below. Give the between-group variance that would be used for this test.

A

B

C

12

5

6

6

2

4

3

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